Question

What transformation has changed the parent function f(x) = log5x to its new appearance shown in the graph below?

Answer 1

Answer:

g(x) = log[5 (x + 4)] - 2

Step-by-step explanation:

In the picture below you can see the blue line is the graph of the function

f(x) = log(5x) and the green line is the graph of the function

g(x) = log[5(x + 4)] - 2

Since the function f passes on the point (2, 1) what we have to do to make sure that the function passes in (-2, -1) is make it go down 2 units, so we subtract 2 to the function f.

We get log(5x) - 2, and then to make the function go left we just need to add 4 to the variable x.

Attention:

• When you add a number to x the function goes left;

• When you subtract a number to x the function goes right;
• When you add a number to the function, the function goes up;
• When you subtract a number to the function, the function goes down.

Then we get a function g(x) = log[5 (x + 4)] - 2.